tempdisagg: converting quarterly time series to daily

Not having a time series at the desired frequency is a common problem for researchers and analysts. For example, instead of quarterly sales, they only have annual sales. Instead of a daily stock market index, they only have a weekly index. While there is no way to fully make up for the missing data, there are useful workarounds: with the help of one or more high frequency indicator series, the low frequency series may be disaggregated into a high frequency series.

The package tempdisagg implements the standard methods for temporal disaggregation: Denton, Denton-Cholette, Chow-Lin, Fernandez and Litterman. Our article on temporal disaggregation of time series in the R-Journal describes the package and the theory of temporal disaggregation in more detail.

The package has been around since eight years, enabling the standard year or quarter to month or quarter disaggregation. With version 1.0, there are now some major new features: disaggregation can be performed from any frequency to any frequency. Also, tempdisagg now supports time series classes other than ts.

Convert between any frequency

tempdisagg can now convert between most frequencies, e.g., it can disaggregate a monthly series to daily. It is no longer restricted to regular conversions, where each low frequency period had the same number of high frequency periods. Instead, a low frequency period (e.g. month) can contain any number of high-frequency periods (e.g. 31, 28 or 29 days). Thanks to Roger Kissling and Stella Sim who have suggested this idea.

We can not only convert months to days, but also years to days, weeks to seconds, or academic years to seconds, or lunar years to hours, … The downside is that the computation time depends on the number of observations. Thus, for longer high-frequency series, the computation may take a while.

In the following, we try to disaggregate quarterly GDP of Switzerland to a hypothetical daily GDP series. The example series are shipped with the package.

##         time    value
## 1 2005-01-01 133101.3
## 2 2005-04-01 136320.4
## 3 2005-07-01 137693.7
## 4 2005-10-01 139475.9
## 5 2006-01-01 139204.7
## 6 2006-04-01 141112.5

Time series can can be stored in data frames

Because we are dealing with daily data, we keep the data in a data.frame, rather than in a ts object. Other time series objects, such as xts and tsibble, are possible as well. For conversion and visualization, we use the tsbox package.

ts_plot(gdp.q, title = "Swiss GDP", subtitle = "real, not seasonally adjusted")

Disaggregation to daily frequency

We use Swiss stock market data as an indicator series to disaggregate GDP. Data of the stock market index, the SMI, is also included in tempdisagg. Weekend and holiday values have been interpolated, because tddoes not allow the presence of missing values.

ts_plot(spi.d, title = "Swiss Performance Index", subtitle = "daily values, interpolated")

The following uses the Chow-Lin method to disaggregate the series. A high rho parameter takes into account that the two series are unlikely to be co-integrated.

m.d.stocks <- td(gdp.q ~ spi.d, method = "chow-lin-fixed", fixed.rho = 0.9)
## Call:
## td(formula = gdp.q ~ spi.d, method = "chow-lin-fixed", fixed.rho = 0.9)
## Residuals:
##    Min     1Q Median     3Q    Max
## -10656  -1760   1076   3796   8891
## Coefficients:
##              Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.320e+03  2.856e+01   46.22   <2e-16 ***
## spi.d       5.512e-02  3.735e-03   14.76   <2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 'chow-lin-fixed' disaggregation with 'sum' conversion
## 59 low-freq. obs. converted to 5493 high-freq. obs.
## Adjusted R-squared: 0.7928 AR1-Parameter:   0.9

And here is the result: A daily series of GDP

gdp.d.stocks <- predict(m.d.stocks)
    ts_c(gdp.d.stocks, gdp.q)
  title = "Daily disaggregated GDP",
  subtitle = "one indicator"

Like with all disaggregation methods in tempdisagg, the resulting series fulfills the aggregation constraint (the resulting series is as long as the indicator, and needs to be shortened for a comparison):

    ts_frequency(gdp.d.stocks, "quarter", aggregate = "sum"),
    end = "2019-07-01"
## [1] TRUE


tsbox 0.2: supporting additional time series classes

The tsbox package makes life with time series in R easier. It is built around a set of functions that convert time series of different classes to each other. They are frequency-agnostic, and allow the user to combine time series of multiple non-standard and irregular frequencies. A detailed overview of the package functionality is given in the documentation page (or in a previous blog-post).

Version 0.2 is now on CRAN and provides a larger number of bugfixes. Non-standard column names are now handled correctly, and non-standard column orders are treated consistently.

New Classes

There are two more time series classes supported: tis time series, from the tis package, and irts time series, from the tseries package.

In order to create an object of these classes, it is sufficient to use the appropriate converter.

E.g., for tis time series:

##       Jan  Feb  Mar  Apr  May  Jun  Jul  Aug  Sep  Oct  Nov  Dec
## 1974  901  689  827  677  522  406  441  393  387  582  578  666 
## 1975  830  752  785  664  467  438  421  412  343  440  531  771 
## 1976  767 1141  896  532  447  420  376  330  357  445  546  764 
## 1977  862  660  663  643  502  392  411  348  387  385  411  638 
## 1978  796  853  737  546  530  446  431  362  387  430  425  679 
## 1979  821  785  727  612  478  429  405  379  393  411  487  574 
## class: tis 

Or for irts time series:

## 1974-01-01 00:00:00 GMT 901 
## 1974-02-01 00:00:00 GMT 689 

Conversion works from all classes to all classes, and we can easily convert these objects to any other time series class, or to a data frame:

x.tis <- ts_tis(fdeaths) 
##         time value 
## 1 1974-01-01   901 
## 2 1974-02-01   689 
## 3 1974-03-01   827 
## 4 1974-04-01   677 
## 5 1974-05-01   522 
## 6 1974-06-01   406 

Class-agnostic functions

Because coercion works reliably and is well tested, we can use it to make functions class-agnostic. If a class-agnostic function works for one class, it works for all:


ts_pc calculates percentage change rates towards the previous period. It works like a ‘generic’ function: You can apply it on any time series object, and it will return an object of the same class as its input.

So, whether we want to smooth, scale, differentiate, chain-link, forecast, regularize or seasonally adjust a series, we can use the same commands to all time series classes. tsbox offers a comprehensive toolkit for the basics of time series manipulation. Here are some additional examples:

ts_pcy(fdeaths)                # pc., comp. to same period of prev. year 
ts_forecast(fdeaths)           # forecast, by exponential smoothing 
ts_seas(fdeaths)               # seasonal adjustment, by X-13 
ts_frequency(fdeaths, "year")  # convert to annual frequency 
ts_span(fdeaths, "-1 year")    # limit time span to final year 

There are many more. Because they all start with ts_, you can use auto-complete to see what’s around. Most conveniently, there is a time series plot function that works for all classes and frequencies:

   `Airline Passengers` = AirPassengers,
   `Lynx trappings` = ts_tis(lynx),
   `Deaths from Lung Diseases` = ts_xts(fdeaths),
   title = "Airlines, trappings, and deaths",
   subtitle = "Monthly passengers, annual trappings, monthly deaths" 

time series plot

tsbox 0.1: class-agnostic time series

The R ecosystem knows a vast number of time series classes: ts, xts, zoo, tsibble, tibbletime or timeSeries. The plethora of standards causes confusion. As different packages rely on different classes, it is hard to use them in the same analysis. tsbox provides a set of tools that make it easy to switch between these classes. It also allows the user to treat time series as plain data frames, facilitating the use with tools that assume rectangular data.

comic by xkcd

The tsbox package is built around a set of functions that convert time series of different classes to each other. They are frequency-agnostic, and allow the user to combine multiple non-standard and irregular frequencies. Because coercion works reliably, it is easy to write functions that work identically for all classes. So whether we want to smooth, scale, differentiate, chain-link, forecast, regularize or seasonally adjust a time series, we can use the same tsbox-command for any time series class.

This blog gives a short overview of the changes introduced in 0.1. A detailed overview of the package functionality is given in the documentation page (or in a previous blog-post).

Keeping explicit missing values

Version 0.1, now on CRAN, brings a large number of bug fixes and improvements. A substantial change involves the treatment of NA values in data frames. Previously, all NAs in data frames were treated as implicit, and were only made explicit by a call to ts_regular.

This has changed now. If you convert a ts object to a data frame, all NA values will be preserved. To replicate previous behavior, apply the ts_na_omit function:

x.ts <- ts_c(mdeaths, austres)

ts_span extends outside of series span

This lays the groundwork for ts_span to be extensible. With extend = TRUEts_span extends a regular series with NA values, up to the specified limits, similar to base window. Like all functions in tsbox, this is frequency-agnostic. For example, in the following, the monthly series mdeaths is extended by monthly NA values, while the quarterly series austres is extended by quarterly NA values.

x.df <- ts_df(ts_c(mdeaths, austres))
ts_span(x.df, end = "1999-12-01", extend = TRUE)

ts_default standardizes column names in a data frame

In rectangular data structures, i.e., in a data.frame, a data.table, or a tibble, tsbox stores one or multiple time series in the ‘long’ format. By default, tsbox detects a value, a time and zero, one or several id columns. Alternatively, the time column and the value column can be explicitly named time and value. If explicit names are used, the column order will be ignored.

While automatic column name detection is useful in interactive mode, it produces unnecessary overhead in longer workflows. The helper function ts_default detects and renames the time and the value column, so that auto-detection will be turned off in subsequent steps (note that the names of the id columns are not affected):

x.df <- ts_df(ts_c(mdeaths, austres))
names(x.df) <- c("a fancy id name", "date", "count")
ts_plot(x.df)  # tsbox is fine with that

ts_summary summarizes time series

ts_summary provides a frequency agnostic summary of a ts-boxable object:

ts_summary(ts_c(mdeaths, austres))
#>        id obs    diff freq      start        end
#> 1 mdeaths  72 1 month   12 1974-01-01 1979-12-01
#> 2 austres  89 3 month    4 1971-04-01 1993-04-01

ts_summary returns a plain data frame that can be used for any purpose. It is also recommended for the extraction of various time series properties, such as start, freq or id:

#> [1] "austres"
#> [1] "1971-04-01"

And a cheatsheet!

Finally, we fabricated a tsbox cheat sheet that summarizes most functionality. Print and enjoy working with time series.

Time Series of the World, Unite!

The R ecosystem knows a ridiculous number of time series classes. So, I decided to create a new universal standard that finally covers everyone’s use case… Ok, just kidding!

tsbox, now freshly on CRAN, provides a set of tools that are agnostic towards existing time series classes. It is built around a set of converters, which convert time series stored as ts, xts, data.frame, data.table, tibble, zoo, tsibble or timeSeries to each other.

To install the stable version from CRAN:


To get an idea how easy it is to switch from one class to another, consider this:

x.ts <- ts_c(mdeaths, fdeaths)
x.xts <- ts_xts(x.ts)
x.df <- ts_df(x.xts)
x.tbl <- ts_tbl(x.df)
x.dt <- ts_tbl(x.tbl)
x.zoo <- ts_zoo(x.dt)
x.tsibble <- ts_tsibble(x.zoo)
x.timeSeries <- ts_timeSeries(x.tsibble)

We jump form good old ts objects toxts, store our time series in various data frames and convert them to some highly specialized time series formats.

tsbox is class-agnostic

Because these converters work nicely, we can use them to make functions class-agnostic. If a class-agnostic function works for one class, it works for all:


ts_scale normalizes one or multiple series, by subtracting the mean and dividing by the standard deviation. It works like a ‘generic’ function: You can apply it on any time series object, and it will return an object of the same class as its input.

So, whether we want to smooth, scale, differentiate, chain-link, forecast, regularize or seasonally adjust a series, we can use the same commands to whatever time series at hand. tsbox offers a comprehensive toolkit for the basics of time series manipulation. Here are some additional operations:

ts_pc(x.ts)                 # percentage change rates 
ts_forecast(x.xts)          # forecast, by exponential smoothing
ts_seas(x.df)               # seasonal adjustment, by X-13
ts_frequency(x.dt, "year")  # convert to annual frequency
ts_span(x.tbl, "-1 year")   # limit time span to final year

tsbox is frequency-agnostic

There are many more. Because they all start with ts_, you can use auto-complete to see what’s around. Most conveniently, there is a time series plot function that works for all classes and frequencies:

  `Airline Passengers` = AirPassengers, 
  `Lynx trappings` = ts_df(lynx), 
  `Deaths from Lung Diseases` = ts_xts(fdeaths),
  title = "Airlines, trappings, and deaths",
  subtitle = "Monthly passengers, annual trappings, monthly deaths"


There is also a version that uses ggplot2 and has the same syntax.

Time series in data frames

You may have wondered why we treated data frames as a time series class. The spread of dplyr and data.table has given data frames a boost and made them one of the most popular data structures in R. So, storing time series in a data frame is an obvious consequence. And even if you don’t intend to keep time series in data frames, this is still the format in which you import and export your data. tsbox makes it easy to switch from data frames to time series and back.

Make existing functions class-agnostic

tsbox includes tools to make existing functions class-agnostic. To do so, the ts_ function can be used to wrap any function that works with time series. For a function that works on "ts" objects, this is as simple as that:

ts_rowsums <- ts_(rowSums)
ts_rowsums(ts_c(mdeaths, fdeaths))

Note that ts_ returns a function, which can be used with or without a name.

In case you are wondering, tsbox uses data.table as a backend, and makes use of its incredibly efficient reshaping facilities, its joins and rolling joins. And thanks to anytime, tsbox will be able to recongnize almost any date format without manual intervention.

So, enjoy some relieve in R’s time series class struggle.


screenshot of

Forecasting GDP with R and

The website aims to be Switzerland’s FRED – a free comprehensive database of Swiss time series. Powered by R and written in Shiny (also using a bit of JavaScript) it allows you to quickly search and explore a large number of data series.

Switzerland’s time series in one place

Similarly to the United States, public data in Switzerland is produced by a large number of different offices, which makes it hard to find any particular series. provides a structured and automatically updated collection of most of these series. We are still working on the data input, but are pretty much complete in the field of Economics.

You can download the data as spreadsheets or graphs, or embed interactive widgets in your website. Alternatively, you can import the data directly into R, using the dataseries package. Install the package from CRAN,


and run the ds function with the id argument that you find on the website:

plot(dataseries::ds("GDP.PBRTT.A.R", "ts"), 
     ylab = "mio CHF, at 2010 prices, s. adj.", 
     main = "Gross Domestic Product")


This will give you an R plot of Switzerland’s GDP. (The data is cached, so calling the function again will not re-download until you restart the R session.)

Live Import of Series to R

In the following, I will use data from to produce a live forecast of Switzerland’s GDP. Each day the model is run, it will be ensured that the latest data is used. That way it is possible to produce a transparent and up-to-date forecast. For the following exercise, I will only use tools from R base, but it is of course possible to use the same data in a more advanced modeling framework.

In order to produce a reasonable forecast, we want to track early information on the business cycle, which is mostly survey data. We will use a question from the SECO Consumer Confidence Survey on current economic performance, the Credit Suisse / Procure Purchasing Managers’ Index and the ETHZ KOF Barometer.

Transforming the data

Getting these indicators from directly into R is easy. Because these data are measured at different frequencies, we need to convert them to the same quarterly frequency as GDP. There are many packages that offer functions for that (e.g., the tempdisagg package has functions to move both to higher or lower frequencies), but I will stick to basic R here:

# Aggregating months to quarters (post updated on May 6, 2017)
to_quarterly <- function(x){
 aggregate(x, nfrequency = 4, FUN = mean)

pmi <- to_quarterly(dataseries::ds("PMI.SA.PM", "ts"))
kof <- to_quarterly(dataseries::ds("KOF.KFBR", "ts"))
csent <- dataseries::ds("CCI.GEPC", "ts")

A plot of these series shows the common trend in these variables and gives you an indication of the business cycle, which may have turned upward in recent months.

plot(cbind(pmi, kof, csent), main = "Business Cycle Indicators")


Since these series are stationary, our left hand side variable should be stationary as well. This is accomplished by calculating percentage change rates of GDP:

gdp.level <- dataseries::ds("GDP.PBRTT.A.R", "ts")
gdp <- (gdp.level / lag(gdp.level, -1)) - 1

ARIMA modelling

R’s workhorse for time series modeling is the arima function, which allows you to construct a univariate or multivariate model of GDP growth. Since the data is seasonally adjusted, a simple autoregressive process (AR1) offers a good benchmark:

# AR1
m0 <- arima(gdp, order = c(1, 0, 0))
fct0 <- predict(m0, n.ahead = 1)$pred
# GDP Growth Q1: +0.3 

If you need advice on which ARIMA model to choose, the information criterions, accessed by the R functions AIC or BIC, can help you to choose a model. Simply take the model with lowest information criterion. The auto.arima function from the forecast package also allows you to do the selection automatically.

We can include our series individually or jointly and estimate a range of different models. A good model (in terms of the AIC information criterion) is the following, which uses PMI and KOF data (but not consumer sentiment data):

dta <- window(cbind(pmi, kof), start = start(pmi), end = end(pmi))
m1 <- arima(window(gdp, start = start(dta)), 
            xreg = window(dta, end = end(gdp)))
fct1 <- predict(m1, n.ahead = 1, 
                newxreg = window(dta, start = tsp(gdp)[2] + 0.25,
                                 end = tsp(gdp)[2] + 0.25)
# GDP Growth Q1: +0.7

The model’s forecast for the first quarter of 2017 is 0.7 – a value that hasn’t been reached for more than two years.

A factor model

If you have multiple indicators at hand, a common problem is multicollinearity, the fact that indicators are correlated, and therefore too many indicators deteriorate the quality of the model estimation.

An easy fix is to use a factor model, where the indicators are summarized in a few factors, which can be calculated by principal components (see Stock and Watson 2002):

# PMI, KOF, Consumer Sentiment, first Principal Component
pca <- prcomp(window(cbind(pmi, kof, csent), start = start(pmi), 
                     end = tsp(gdp)[2] + 0.25),
             scale. = TRUE)
dta.pca <- ts(pca$x[, 'PC1'], start = start(pmi), frequency = 4)

m2 <- arima(window(gdp, start = start(dta)), 
            xreg = window(dta.pca, end = end(gdp)))
fct2 <- predict(m2, n.ahead = 1, 
                newxreg = window(dta.pca, start = tsp(gdp)[2] + 0.25)
# GDP Growth Q1: +0.7

Again, we get a forecast value of 0.7. Overall, survey data indicates that the economy is well on track. Let’s do a graphical comparison of our forecasts:

# skeletons to include forecasts 
gdp.fct0 <- window(gdp, extend = TRUE, end = tsp(gdp)[2] + 0.25)
gdp.fct1 <- gdp.fct2 <- gdp.fct0

# plug forecasts into skeletons
window(gdp.fct0, start = end(gdp.fct0)) <- fct0
window(gdp.fct1, start = end(gdp.fct1)) <- fct1
window(gdp.fct2, start = end(gdp.fct2)) <- fct2

ts.plot(window(cbind(gdp, gdp.fct0, gdp.fct1, gdp.fct2), 
               start = 2010), 
        col = 1:4, ylab = "quarterly growth rates, s. adj.", 
        main = "GDP Forecasts")
legend("topright", legend = c("GDP Growth Rate", "AR 1 Forecast", 
                              "PMI, KOF", "Principal Component"), 
       lty = 1, col = 1:4, bty = "n")


Publication of first quarter GDP is on June 1, 2017. See you in a month!

seasonal 1.3: A Better Way to Seasonal Adjustment Diagnostics

The R package seasonal makes it easy to use X-13ARIMA-SEATS, the seasonal adjustment software by the United States Census Bureau. Thanks to the x13binary package, installing it from CRAN is now as easy as installing any other R package:


The latest version 1.3 comes with a new udg function and a customizable summary method, which give power users of X-13 a convenient way to check the statistics that are of their interest. For a full list of changes, see the package NEWS.

A generalized way to access diagnostics

Version 1.3 offers a generalized way to access diagnostic statistics. In seasonal, it was always possible to use all options of X-13 and access all output series. Now it is easy to access all diagnostics as well.

The main new function is udg, named after the X-13 output file which it is reading. Consider a simple call to seas (the main function of the seasonal package) that uses the X-11 seasonal adjustment method:

m <- seas(AirPassengers, x11 = "")

The udg function returns a list containing 357 named diagnostics. They are properly type-converted, so they can be directly used for further analysis within R.

If we ask for a specific statistic, such as the popular X-11 M statistics, the result will be simplified to a numeric vector (see ?udg for additional options):

udg(m, c("f3.m01", "f3.m02", "f3.m03", "f3.m04"))

## f3.m01 f3.m02 f3.m03 f3.m04 
##  0.041  0.042  0.000  0.283

There are also some new wrappers for commonly used statistics, such as AICBIC, logLik or qs, which use the udg function.

A customizable summary

The new functionality paves the way for a customizable summary method for seas objects. For example, if we want to add the M statistics for X-11 adjustments to the summary, we can write:

summary(m, stats = c("f3.m01", "f3.m02", "f3.m03", "f3.m04"))

## Call:
## seas(x = AirPassengers, x11 = "")
## Coefficients:
##                     Estimate Std. Error z value Pr(>|z|)    
## Weekday           -0.0029497  0.0005232  -5.638 1.72e-08 ***
## Easter[1]          0.0177674  0.0071580   2.482   0.0131 *  
## AO1951.May         0.1001558  0.0204387   4.900 9.57e-07 ***
## MA-Nonseasonal-01  0.1156204  0.0858588   1.347   0.1781    
## MA-Seasonal-12     0.4973600  0.0774677   6.420 1.36e-10 ***
## ---
## Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
## X11 adj.  ARIMA: (0 1 1)(0 1 1)  Obs.: 144  Transform: log
## AICc: 947.3, BIC: 963.9  QS (no seasonality in final):    0  
## Box-Ljung (no autocorr.): 26.65   Shapiro (normality): 0.9908  
## f3.m01: 0.041  f3.m02: 0.042  f3.m03: 0  f3.m04: 0.283 

Note the new line at the end, which shows the M statistics.

If we want to routinely consider these statistics in our summary, we can set the seas.stats option accordingly:

options(seas.stats = c("f3.m01", "f3.m02", "f3.m03", "f3.m04"))

This will change the default behavior, and


will return the same output as above. To restore the default behavior, set the option back to NULL.

options(seas.stats = NULL)

Like peanut butter and jelly: x13binary and seasonal

This post was written by Dirk Eddelbuettel and Christoph Sax and posted by both author’s respective blogs.

The seasonal package by Christoph Sax brings a very featureful and expressive interface for working with seasonal data to the R environment. It uses the standard tool of the trade: X-13ARIMA-SEATS. This powerful program is provided by the statisticians of the US Census Bureau based on their earlier work (named X-11 and X-12-ARIMA) as well as the TRAMO/SEATS program by the Bank of Spain. X-13ARIMA-SEATS is probably the best known tool for de-seasonalization of timeseries, and used by statistical offices around the world.

Sadly, it also has a steep learning curve. One interacts with a basic command-line tool which users have to download, install and properly reference (by environment variables or related means). Each model specification has to be prepared in a special ‘spec’ file that uses its own, cumbersome syntax.

As seasonal provides all the required functionality to use X-13ARIMA-SEATS from R — see the very nice seasonal demo site — it still required the user to manually deal with the X-13ARIMA-SEATS installation.

So we decided to do something about this. A pair of GitHub repositories provide both the underlying binary in a per-operating system form (see x13prebuilt) as well as a ready-to- use R package (see x13binary) which uses the former to provide binaries for R. And the latter is now on CRAN as package x13binary ready to be used on Windows, OS-X or Linux. And the seasonal package (in version 1.2.0 – now on CRAN – or later) automatically makes use of it. Installing seasaonal and x13binary in R is now as easy as:


which opens the door for effortless deployment of powerful deasonalization. By default, the principal function of the package employs a number of automated techniques that work well in most circumstances. For example, the following code produces a seasonal adjustment of the latest data of US retail sales (by the Census Bureau) downloaded from Quandl:


url <- ""
rs <- ts(read.csv(url)$Value/1e3, start = c(1992, 1), frequency = 12)

m1 <- seas(rs)

plot(m1, main = "Retail Trade: U.S. Total Sales", 
     ylab = "USD (in Billions)")

This tests for log-transformation, performs an automated ARIMA model search, applies outlier detection, tests and adjusts for trading day and Easter effects, and invokes the SEATS method to perform seasonal adjustment. And this is how the adjusted series looks like:


Of course, you can access all available options of X-13ARIMA-SEATS as well. Here is an example where we adjust the latest data for Chinese exports (as tallied by the US FED), taking into account the different effects of Chinese New Year before, during and after the holiday:

url <- ""
xp <- ts(read.csv(url)$VALUE/1e9, start = c(1981, 1), frequency = 12)

m2 <- seas(window(xp, start = 2000), 
  xreg = cbind(
    genhol(cny, start = -7, end = -1, center = "calendar"),
    genhol(cny, start = 0, end = 7, center = "calendar"), 
    genhol(cny, start = 8, end = 21, center = "calendar")),
  regression.aictest = c("td", "user"),
  regression.usertype = "holiday")

plot(m2, main = "Goods, Value of Exports for China", 
     ylab = "USD (in Billions)")

which generates the following chart demonstrating a recent flattening in export activity measured in USD.


We hope this simple examples illustrates both how powerful a tool X-13ARIMA-SEATS is, but also just how easy it is to use X-13ARIMA-SEATS from R now that we provide the x13binary package automating its installation.

Shiny-based Online Tool for X-13 Seasonal Adjustment: New Features

The R package seasonal makes it easy to use X-13ARIMA-SEATS, the seasonal adjustment software by the U.S. Census Bureau. In a previous post, I wrote about, a Shiny-based website showcasing the use of seasonal. Even if you are not using R, the website allows you to upload and adjust your own series, without the need for any software installation.

The latest version of comes with several new features:

Live Parsing of X-13 spc Files

The main new feature is a live parser of X-13 spc files. Changes in the Options, triggered by the pull-down menus, or changes in the R Call, are reflected in an updated X-13 Call. On the other hand, changes in the X-13 Call will be reflected in updates in the Options and the R Call.

manipulate the X-13 spec file

Interactively manipulate the X-13 spec file or the R call

This brings interesting new possibilities:

  • Non-R-users may use the website to generate spc files, which they can use in any software that includes X-13ARIMA-SEATS.
  • People familiar with X-13 may use the spc syntax to learn about the syntax of the R-package seasonal.
  • People familiar with the R-package seasonal may use it learn about the spc syntax.

New Upload/Download Dialog

The upload/download feature has been reworked. A button on the top-right corner opens a new upload and download dialog.

New upload/download dialog

New upload/download dialog

Both XLSX and CSV formats are supported. You can upload and adjust your own monthly or quarterly time series. All data will be permanently deleted after your session.

Nice Summary

The summary, previously just the printed output of the R-function summary, has been overhauled. Colored flags indicate the significance level of the coefficients, reddish colors indicate warning signs from the tests.

New Summary

New Summary

New Online Tool for Seasonal Adjustment

Seasonal adjustment of time series can be a hassle. The softwares used by statistical agencies (X-13, X-12, TRAMO-SEATS) have tons of fantastic options, but the steep learning curve prevents users from taking advantage of the functionality of these packages, or from using them at all.

The R package seasonal simplifies the task by providing an interface to X-13, the newest seasonal adjustment software by the US Census Bureau. It combines and extends the capabilities of the older X-12ARIMA and TRAMO-SEATS software packages. The most simple use of seasonal requires the application of the main function to a time series, which invokes automated procedures that work well in many circumstances:


A new shiny based website is showcasing the use of seasonal and allows for online adjustment of time series, without the need to download and install seasonal. The AirPassengers series is set as the default series, but can be replaced by any uploaded series. There are other demo series that show the use of the software to adjust Indian Diwali or Chinese New Year effects.

The site allows to adjust most parameters of X-13, and to view and download a substantial part of its output. Frequently used options can be chosen from a drag and drop menu, while less often used options can be chosen by manipulating the R-Call itself.

Here are some of the most interesting features of the website:

Frequently Used Options

Frequently used options of X-13 can be modified using the drop down selectors. Each change will result in a re-estimation of the seasonal adjustment model. The R-call, the output and the summary are updated accordingly.

Frequently Used Options

Choosing the Output

A substantial part of the output of X-13ARIMA-SEATS can be shown on the website. Click and drag to zoom into the graph. Double click to restore the original view.

A substantial part of the output of X-13ARIMA-SEATS can be shown on the website.

Manipulating the R-Call

The R-Call to seasonal can be modified and run online. In the picture below, the ARIMA model has been adjusted to include an autoregressive parameter of order 2. Press the button to execute the modified call.

Manipulating the R Call

Upload and Download

User defined series can be uploaded, importing from Excel or CSV. Also, all viewable series can be downloaded as Excel or CSV.

Upload and Download

Chinese New Year, Indian Diwali

Chinese New Year or Indian Diwali support is included out of the box and can be selected from the drop down menu. Adjustment for these holidays is as easy as adjusting Easter effects.

Adjusting Chinese New Year or Indian Diwali Effects

Running X-13 Examples Online

The examples from the official manual of X-13 can be run directly on the website. The collection of examples can found here.

Examples of X 13ARIMA SEATS in R

Try it out!

Adjusting Chinese New Year Effects in R is Easy

The Spring Festival is the most important holiday in China and many other Asian countries. Traditionally, the holiday starts on Chinese New Year’s Eve, and lasts to the Lantern Festival on the 15th day of the first month of the lunisolar calendar. The Chinese New Year is celebrated either in January or in February of the Gregorian calendar.

Because of its importance, Chinese New Year seriously distorts monthly time series, which are usually reported according to the Gregorian calendar. Unlike Easter, Chinese New Year does not affect quarterly time series, as it always falls in the first quarter.

The standard software packages for seasonal adjustment, X-12-ARIMA and X-13-ARIMA-SEATS (developed by the U.S. Census Bureau) or Tramo Seats (developed by the Bank of Spain) have a built-in adjustment procedure for Easter holiday, but not for Chinese New Year. However, all packages allow for the inclusion of user defined variables, and the Chinese New Year can be modeled as such.

The R package seasonal

With the R package seasonal, generating and including such a series is easy. We will use it in the following to seasonally adjust and remove Chinese New Year effects from the nominal dollar value of imports to China. seasonal is an interface to X-13ARIMA-SEATS; for more information and installation details, see here.

Chinese imports are included as an example series in seasonal. As the series has a very different seasonal pattern before 2000, we focus on the later period. (Adjusting the whole series in one step is possible, but for good results one should manually model the seasonal break.)

data(cntrade)  # contains imports ('imp') and exports ('exp') of China
imp <- window(imp, start = 2000)  # this shortens the series

seasonal includes the genhol() function, a R version of the equally named software utility by the U.S. Census Bureau. Using the dates of the Chinese New Year as an input, it produces a time series with the deviations from the monthly means. Here we are assuming that the holiday starts on New Year’s Eve and lasts for one week.

data(holiday)  # dates of Chinese New Year and Easter, included in seasonal
cny.ts <- genhol(cny, start = -1, end = 6, center = "calendar")

In 2014, only two days in January were affected by the holiday (New Year’s Eve and New Year’s Day). 75% of the holiday fell into February. Thus, January was affected slightly less than average, February slightly more. This is very different from 2012, when the holiday completely fell into January.

       Jan   Feb   Mar   Apr   May   Jun   Jul   Aug   Sep   Oct   Nov   Dec
2011 -0.26  0.26  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
2012  0.74 -0.74  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
2013 -0.26  0.26  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00
2014 -0.01  0.01  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00  0.00

Including user defined regressors

The time series cny.ts can be included in the main seasonal adjustment. The automated procedures of X-13ARIMA-SEATS can be applied to the imp series in the following way:

m1 <- seas(imp, xreg = cny.ts, regression.usertype = "holiday", x11 = list())

## Call:
## seas(x = imp, xreg = cny.ts, regression.usertype = "holiday", 
##     x11 = list())
## Coefficients:
##                   Estimate Std. Error z value Pr(>|z|)    
## cny.ts            -0.18104    0.01548  -11.70  < 2e-16 ***
## Weekday            0.00514    0.00104    4.94  7.8e-07 ***
## LS2008.Nov        -0.37584    0.04745   -7.92  2.3e-15 ***
## MA-Nonseasonal-01  0.39776    0.07202    5.52  3.3e-08 ***
## MA-Seasonal-12     0.72749    0.06428   11.32  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ARIMA structure: (0 1 1)(0 1 1)   Number of obs.: 169   Transform: log
## AICc: 1.6e+03, BIC: 1.62e+03   QS seas. test (adj. series):   0  
## Box-Ljung (no autocorr.): 33.6 .  Shapiro (normality): 0.978 **

With xreg, arbitrary user defined regressors can be included, regression.usertype = "holiday" ensures that the final series does not include the regression effect. We also have chosen X11 as the decomposition method.

Unsurprisingly, the summary reveals a highly significant Chinese New Year effect. As the automatic model has been estimated on the logarithmic series, the coefficient of -0.18 indicates that New Year in 2012 has lowered imports by approximately 0.74 * 18 = 13%. The automatic procedure has also detected weekday effects and a level shift during the financial crisis.

Multiple regressors

We can do even better by using more than one user defined regressors, one for the pre-New-Year period and one for the post-New-Year period (thanks, Freya Beamish):

pre_cny <- genhol(cny, start = -6, end = -1, frequency = 12, center = "calendar")
post_cny <- genhol(cny, start = 0, end = 6, frequency = 12, center = "calendar")
m2 <- seas(x = imp, xreg = cbind(pre_cny, post_cny), regression.usertype = "holiday", 
           x11 = list())

## Call:
## seas(x = imp, xreg = cbind(pre_cny, post_cny), regression.usertype = "holiday", 
##     x11 = list())
## Coefficients:
##                    Estimate Std. Error z value Pr(>|z|)    
## pre_cny            0.070843   0.019199    3.69  0.00022 ***
## post_cny          -0.241043   0.020816  -11.58  < 2e-16 ***
## Weekday            0.005233   0.000943    5.55  2.9e-08 ***
## LS2008.Nov        -0.357887   0.045790   -7.82  5.5e-15 ***
## MA-Nonseasonal-01  0.331626   0.073967    4.48  7.3e-06 ***
## MA-Seasonal-12     0.687479   0.065740   10.46  < 2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## ARIMA structure: (0 1 1)(0 1 1)   Number of obs.: 169   Transform: log
## AICc: 1.59e+03, BIC: 1.61e+03   QS seas. test (adj. series):0.75  
## Box-Ljung (no autocorr.): 37.6 *  Shapiro (normality): 0.984 *

adjusted and unadjusted series

Chinese imports: adjusted and unadjusted series

There are actually two kind of New Year effects: Until New Year’s Eve, import activity is higher than usual. During the holiday, it is lower. By including two regressors, these opposite effects can be modeled. Note that the negative effect is more pronounced than the positive one.

Manual refinements

The model could be further refined. With the static() function, a non-automatic version of the previous call can be extracted. It can be copy-pasted and used for further manipulations.


## seas(x = imp, xreg = cbind(pre_cny, post_cny), regression.usertype = "holiday", 
##     x11 = list(), regression.variables = c("td1coef", "ls2008.Nov"
##     ), arima.model = "(0 1 1)(0 1 1)", regression.aictest = NULL, 
##     outlier = NULL, transform.function = "log")

The inspect() function opens an interactive window that allows for the manipulation of a number of arguments. With each change, the adjustment process and the visualizations are recalculated. (This only works with R Studio.)


After some playing around, we would probably stay with the two regressor adjustment model from above:

m2 <- seas(x = imp, xreg = cbind(pre_cny, post_cny), regression.usertype = "holiday", 
           x11 = list(), regression.variables = c("td1coef", "ls2008.Nov"), 
           arima.model = "(0 1 1)(0 1 1)", regression.aictest = NULL, 
           outlier = NULL, transform.function = "log")

It’s far form perfect. Normality statistics are bad, and there may be some traces of autocorrelation. On the other hand, the seasonal component is stable and revisions are small.

Comparing the series

Was it worth the pain? The following graph shows the same seasonal adjustment with and without the Chinese New Year adjustment:

m3 <- seas(x = imp, x11 = list(), regression.variables = c("td1coef", "ls2008.Nov"), 
           arima.model = "(0 1 1)(0 1 1)", regression.aictest = NULL, outlier = NULL, 
           transform.function = "log")

ts.plot(diff(log(cbind(final(m2), final(m3)))), col = c("red", "blue"), 
        lwd = c(2, 1))
Comparison of adjusted and unadjusted time series

Not adjusting Chinese New Year seriously distorts the time series

In 2012, we would have concluded that imports have plumped in January, soared in February and plumped again in March (blue line). With the adjustment, we rightly conclude that there was no such craziness (red line).

ts.plot(final(m2), final(m1), col = c("red", "blue"), lwd = c(2, 1))
Stagnating Imports

Chinese imports have stagnated this January

How useful is the two regressor model? Most of the time, the single regressor model performs reasonably well and leads to results similar to the two regressors model. This year, however, the Lunar New Year fell on January 31. As people were importing more in the pre-New-Year period, January imports were actually affected by a positive New Year effect. The right adjustment would be to correct the numbers downward! With the one regressor model, we would wrongly conclude that imports have soared (blue line). In fact, they have actually stagnated (red line).